Vainshtein mechanism in Gauss-Bonnet gravity and Galileon aether

Abstract

We derive field equations of Gauss-Bonnet gravity in 4 dimensions after dimensional reduction of the action and demonstrate that in this scenario Vainshtein mechanism operates in the flat spherically symmetric background. We show that inside this Vainshtein sphere the fifth force is negligibly small compared to the gravitational force. We also investigate stability of the spherically symmetric solution, clarify the vocabulary used in the literature about the hyperbolicity of the equation and the ghost-Laplacian stability conditions. We find superluminal behavior of the perturbation of the field in the radial direction. However, because of the presence of the non linear terms, the structure of the space-time is modified and as a result the field does not propagate in the Minkowski metric but rather in an "aether" composed by the scalar field $\pi (r)$. We thereby demonstrate that the superluminal behavior does not create time paradoxes thank to the absence of Causal Closed Curves. We also derive the stability conditions for Friedmann Universe in context with scalar and tensor perturbations.

9 pages, 5 figures, references added, more details on the cosmological analysis included, results and conclusions unchanged, final version to appear in PRD

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Cited by in corpus (12)

• Massive Gravity
• Dynamical analysis of generalized Galileon cosmology
• New perspective for black hole thermodynamics in Gauss-Bonnet-Born-Infeld massive gravity
• Galileon Radiation from Binary Systems
• Screening the fifth force in the Horndeski's most general scalar-tensor theories
• Light mass galileons: Cosmological dynamics, mass screening and observational constraints
• $D\to 4$ Einstein-Gauss-Bonnet Gravity and Beyond
• Casimir Dark Energy, Stabilization of the Extra Dimensions and Gauss-Bonnet Term
• Probing Screening and the Graviton Mass with Gravitational Waves
• Effects of the external string cloud on the Van der Waals like behavior and efficiency of AdS-Schwarzschild black holes in massive gravity
• Global asymptotic dynamics of the cubic galileon interacting with dark matter
• Purely metric Horndeski theories and spontaneous curvaturization of black holes